Problem: Rewrite as a simplified fraction. ${2.2\overline{48} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2248.4848...\\ 10x &= 22.4848...\end{align*}}$ Subtracting the two equations, we have: ${990x = 2226}$ ${x = \dfrac{2226}{990}} $ ${x = \dfrac{371}{165}} \text{or} {2 \dfrac{41}{165}}$